So I turned off distance fields in the project setting just to see what would happen, and the blobby shadows on that particular object is still there.
If I move it away from the surrounding static geometry, it goes away (but of course I need to be in that location). If I make the surrounding geometry also moveable, they also gain blobby shadows from somewhere.
If I move the static directional light in the scene, the blobby shadows disappear… but they return after baking! (And again, they only show on MOVEABLE objects.)